Solve for $x$ : $5x^2 - 30x + 40 = 0$
Dividing both sides by $5$ gives: $ x^2 {-6}x + {8} = 0 $ The coefficient on the $x$ term is $-6$ and the constant term is $8$ , so we need to find two numbers that add up to $-6$ and multiply to $8$ The two numbers $-4$ and $-2$ satisfy both conditions: $ {-4} + {-2} = {-6} $ $ {-4} \times {-2} = {8} $ $(x {-4}) (x {-2}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -4) (x -2) = 0$ $x - 4 = 0$ or $x - 2 = 0$ Thus, $x = 4$ and $x = 2$ are the solutions.